Justice Minister Ayelet Shaked and Internal Security Minister Gilad Erdan said in a joint statement they had met earlier in the day with senior Facebook executives who were informed of their intention.
Shaked and Erdan said the legislation would aim to make it illegal to publish "offensive content" such as "encouraging terror attacks, shaming, insulting public officials and slandering".
Internet giants such as Facebook and Google could be held accountable, they said.
In their meeting with the executives, they sought the removal of inciting content within 24 hours, as Facebook does in the European Union, said the statement.
This would be backed by a law that blocks concent inciting "terror" and ensures its "complete removal, similar to laws in Australia and France".
Israel maintains that online content has played a significant role in fuelling a wave of Palestinian attacks that broke out in October 2015.
The violence has killed at least 209 Palestinians, 32 Israelis, two Americans, an Eritrean and a Sudanese.
Israeli authorities say most of the Palestinians were killed as they carried out knife, gun or car-ramming attacks.
Others were killed in clashes with security forces or by Israeli air strikes in the Gaza Strip.
According to the Wednesday statement, the ministers said that "in the latest wave of terror there has been a direct link between online incitement and the so-called 'lone wolf terror' attacks."
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